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Glacial ocean circulation and stratification explainedby reduced
atmospheric temperatureMalte F. Jansena,1
aDepartment of the Geophysical Sciences, The University of
Chicago, Chicago, IL 60637
Edited by Mark H. Thiemens, University of California, San Diego,
La Jolla, CA, and approved November 7, 2016 (received for review
June 27, 2016)
Earth’s climate has undergone dramatic shifts between glacial
andinterglacial time periods, with high-latitude temperature
changeson the order of 5–10 ◦C. These climatic shifts have been
asso-ciated with major rearrangements in the deep ocean
circulationand stratification, which have likely played an
important role inthe observed atmospheric carbon dioxide swings by
affecting thepartitioning of carbon between the atmosphere and the
ocean.The mechanisms by which the deep ocean circulation
changed,however, are still unclear and represent a major challenge
to ourunderstanding of glacial climates. This study shows that
vari-ous inferred changes in the deep ocean circulation and
stratifica-tion between glacial and interglacial climates can be
interpretedas a direct consequence of atmospheric temperature
differences.Colder atmospheric temperatures lead to increased sea
ice coverand formation rate around Antarctica. The associated
enhancedbrine rejection leads to a strongly increased deep ocean
strati-fication, consistent with high abyssal salinities inferred
for thelast glacial maximum. The increased stratification goes
togetherwith a weakening and shoaling of the interhemispheric
over-turning circulation, again consistent with proxy evidence for
thelast glacial. The shallower interhemispheric overturning
circula-tion makes room for slowly moving water of Antarctic
origin,which explains the observed middepth radiocarbon age
maximumand may play an important role in ocean carbon storage.
LGM | AMOC | stratification | cooling | sea-ice
The deep ocean today is ventilated mainly by two watermasses.
North Atlantic deep water (NADW) is formed inthe North Atlantic
before flowing southward at a depth of about2–3 km and eventually
rising back up to the surface in theSouthern Ocean. Antarctic
bottom water (AABW) is formedaround Antarctica and spreads
northward into the abyssal basins.The AABW that makes it into the
Atlantic then slowly upwellsinto the lower NADW before returning
southward and resur-facing again around Antarctica (1, 2). The
glacial equivalentof NADW was likely confined to shallower depths,
leavingmore of the deep Atlantic filled with water masses
originat-ing primarily from around Antarctica (3–5). Moreover, the
twowater masses appear more distinct, with less mixing betweenthem
(6).
Multiple studies have pointed toward the potential impor-tance
of sea ice and surface buoyancy fluxes around Antarc-tica in
controlling changes in the deep ocean stratification andcirculation
between the present and Last Glacial Maximum(LGM) (7–11).
Specifically, we recently showed that enhancedbuoyancy loss around
Antarctica is expected to lead to anincrease in the abyssal
stratification, an upward shift of NADW,and a clearer separation
between NADW and southward-flowingAABW (11)—all in agreement with
inferences made for differ-ences in circulation and stratification
between the present andLGM (3, 6, 12, 13). This gives rise to the
hypothesis that strongcooling around Antarctica led to an increased
net freezing rate.The resulting net salt flux into the ocean
amounts to an increasedbuoyancy loss, which then led to the
observed changes in deepocean stratification and circulation. This
hypothesis is tested inthis study.
We test the connection between atmospheric temperatureand ocean
circulation and stratification changes, using idealizednumerical
simulations, which allow us to isolate the proposedmechanism. We
use a coupled ocean–sea-ice model, with atmo-spheric temperature,
winds, and evaporation–precipitation pre-scribed as boundary
conditions (Materials and Methods). Themodel uses an idealized
continental configuration resembling theAtlantic and Southern
Oceans, where the most elemental circu-lation changes have been
inferred (3, 5, 6, 12).
ResultsWe first focus on the model’s ability to reproduce key
featuresof the modern (interglacial) ocean state and circulation.
Fig. 1Ashows the sea surface temperature (SST) over the simu-lated
domain, with boundary conditions resembling present-dayatmospheric
forcing. The chosen forcing gives SSTs in broadagreement with
observations, varying from about 28◦C in thetropics to the freezing
point (∼ −2 ◦C) around Antarctica, wheresea ice forms (Fig. 1A,
white contours). The North Atlantic issomewhat warmer and ice free.
Fig. 2 shows zonally averageddepth–latitude sections of potential
temperature (Fig. 2A) andsalinity (Fig. 2C), which reproduce the
basic features observedin the present-day Atlantic. In particular,
we see a tongue ofsalty water at middepth, penetrating southward
into the South-ern Ocean and leading to a reversal of the salinity
stratifica-tion in the abyss (2). The associated overturning
streamfunc-tion (Fig. 3A) reveals that this salty tongue is
associated withNADW that flows southward as part of the Atlantic
meridionaloverturning circulation (AMOC). Below the clockwise
AMOCcell lies an anticlockwise abyssal cell, representing the
pathwayof AABW. The peak overturning transports of +17.5
Sverdrup
Significance
To understand climatic swings between glacial and
interglacialclimates we need to explain the observed fluctuations
inatmospheric carbon dioxide (CO2), which in turn are mostlikely
driven by changes in the deep ocean circulation. Thisstudy presents
a model for differences in the deep oceancirculation between
glacial and interglacial climates consis-tent with both our
physical understanding and various proxyobservations. The results
suggest that observed changes inocean circulation and
stratification are caused directly byatmospheric cooling or
warming, which has important impli-cations for our interpretation
of glacial–interglacial transi-tions. In particular, the direct
link between atmospheric tem-perature and ocean circulation changes
supports the notion ofa positive feedback loop between atmospheric
temperature,ocean circulation, and atmospheric CO2.
Author contributions: M.F.J. designed research, performed
research, analyzed data, andwrote the paper.
The author declares no conflict of interest.
This article is a PNAS Direct Submission.1Email:
[email protected].
This article contains supporting information online at
www.pnas.org/lookup/suppl/doi:10.1073/pnas.1610438113/-/DCSupplemental.
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mailto:[email protected]://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1610438113/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1610438113/-/DCSupplementalhttp://www.pnas.org/cgi/doi/10.1073/pnas.1610438113http://crossmark.crossref.org/dialog/?doi=10.1073/pnas.1610438113&domain=pdf
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Fig. 1. (A and B) Sea surface temperature (colors) and sea-ice
concentration(white contours), for simulations with boundary
conditions representingpresent-day conditions (A) and LGM
conditions with reduced atmospherictemperature (B). Contour
interval for sea-ice concentration is 20%.
(SV) and −5.2 SV are roughly consistent with the observed rateof
NADW formation and the transport of AABW into the NorthAtlantic (1,
2).
We now analyze the response of the model’s equilibrium solu-tion
to a reduction in atmospheric temperature. Consistent with
Fig. 2. (A–D) Zonal mean temperature (A and B) and salinity (C
and D) for simulations with boundary conditions representing
present-day forcing (A andC) and simulations with reduced
atmospheric temperature resembling LGM conditions (B and D).
Contour intervals are 1◦C in A and B and 0.05 g/kg in Cand D. Note
that the colorbar ranges have been cropped to focus on the deep
ocean.
proxy data for the LGM, the prescribed atmospheric cooling
ispolar amplified, ranging from 2◦C in the tropics to 6◦C
aroundAntarctica (14, 15). All other boundary conditions are held
fixed.The reduction in atmospheric temperature leads to a
reductionin ocean surface temperature and an expansion of sea ice
aroundAntarctica, as well as the appearance of sea ice in the
NorthAtlantic (Fig. 1B). Moreover, the model suggests a cooling
andsalinification of AABW, leading to a strong salt stratification
inthe deep ocean, which replaces the reversed salinity
stratifica-tion observed with present-day forcing (Fig. 2B). The
strong saltstratification is consistent with pore-fluid data for
the LGM (12).(To compare the absolute salinity values here to those
inferredfor the LGM, one needs to account for the increased bulk
oceansalinity resulting from the eustatic drop in sea level, which
is notincluded in the simulations and would add around 1 g/kg
glob-ally.) The AMOC cell weakens and shoals (Fig. 3B), again
consis-tent with inferences for the LGM (3–5). The abyssal cell
slightlystrengthens and becomes somewhat more confined to the
abyss,leading to an increased separation between the two
overturningcells, which may have played an important role in the
increasedocean carbon storage (6).
In the real ocean the abyssal overturning cell is
distributedover multiple basins and currently overlaps in depth and
densitywith the AMOC cell, leading to a continuous exchange of
waterbetween the two cells in the Southern Ocean (1, 2).
Whereasthis interbasin overlap between the present-day overturning
cellscannot be modeled in a single-basin model, the simulated
con-traction of both the AMOC and abyssal cells is likely to
berobust (11). In a multibasin configuration, this contraction
ofboth cells is expected to remove or reduce the overlap betweenthe
two cells, thus generating a more isolated abyssal water mass.The
rearrangement of the overturning circulation would likely
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Fig. 3. (A and B) Meridional overturning streamfunction (colors)
and potential density referenced to 2 km depth (black lines), for
simulations with boundaryconditions representing present-day
forcing (A) and LGM conditions with reduced atmospheric temperature
(B). The overturning streamfunction is computedfrom the sum of the
Eulerian zonal mean velocity and the parameterized eddy-induced
bolus velocity. [Note that the isopycnal overturning transport
includesan additional component associated with standing meanders
(11), which is not included in Fig. 3. The contribution of standing
meanders largely cancels theapparent diapycnal zonal-mean transport
in the channel region.]
resemble that sketched in Ferrari et al. (9), although the
mecha-nism proposed here is somewhat different.
The changes in the deep ocean circulation and stratificationhere
result from an increased buoyancy loss rate around Antarc-tica,
which in turn results primarily from enhanced brine rejec-tion
associated with sea-ice formation and export. Sea-ice exportis
proportional to the product of the ice load (here defined as
thetime- and zonal-mean mass of sea-ice and snow per unit area)and
equatorward transport velocity. Both increase as the atmo-spheric
temperature is reduced, with the dominant role playedby differences
in the ice load, which (near its maximum) goesup from about 300
kg/m2 in the “present” simulation to about800 kg/m2 in the “LGM”
simulation. The ice export velocity alsoincreases, as sea ice
extends farther northward where the west-erly winds are stronger.
As a result of the larger ice load andexport velocity, the peak ice
export rate from around Antarcticaincreases from about 3 ×107 kg/s
to about 14 ×107 kg/s.
To compute the effective net buoyancy loss around Antarc-tica it
is important to consider the nonlinearity of the equationof state
and in particular the pressure dependence of the ther-mal expansion
coefficient (16). If surface buoyancy fluxes arecomputed using the
surface haline and thermal expansion coef-ficients, virtually no
buoyancy loss around Antarctica is found inthe present-day–like
simulation. This lack of buoyancy loss wouldappear to be at odds
with the presence of an abyssal cell and thetransformation of
upwelling circumpolar deep water (CDW) toAABW. The apparent
contradiction can be resolved by notingthat the density increase
associated with the transformation ofCDW to AABW is dominated by a
cooling and counteracted bya freshening. Whereas cooling has a
small effect on surface den-sities at cold temperatures, the
temperature effect is amplifiedas a water parcel sinks into the
deep ocean. We can estimatethe effect of heat and salt fluxes on a
parcel at depth by com-puting buoyancy fluxes based on changes in
potential densitiesreferenced to 2 km depth (consistent with the
potential densitiesshown in Fig. 3), which yields an integrated
surface buoyancyloss rate around Antarctica for the
present-day–like simulationof about 4.4 ×103 m4· s−3 (Materials and
Methods). In the LGMsimulation the integrated surface buoyancy loss
rate increases to2.1× 104 m4· s−3.
The larger buoyancy loss rate around Antarctica in the
LGMsimulation gives rise to the observed changes in deep ocean
cir-culation and stratification. Because surface buoyancy loss
around
Antarctica has to be balanced by vertical diffusion in the
basin,the deep ocean stratification is expected to depend
approxi-mately linearly on the buoyancy loss rate (11). This
relationshipexplains the increase in the deep ocean stratification
between thepresent and LGM simulations (although a quantitative
compar-ison of changes in buoyancy loss and stratification is
somewhatcomplicated by the nonlinearity in the equation of state).
Theincreased stratification in the LGM then leads to an upward
shiftof NADW, consistent with the results of Jansen and Nadeau
(11).
Sensitivity ExperimentsTo test the robustness of the results to
additional modificationsin the boundary conditions, we consider a
number of sensitivityexperiments, varying the wind stress and the
vertical turbulentdiffusivity, as well as the spatial structure of
atmospheric temper-ature change. The results of these simulations
are summarized inTable 1 and are briefly discussed in the
following.
In a seminal paper, Toggweiler et al. (17) proposed an
equa-torward shift in the latitude of the Southern Hemisphere
sur-face westerlies as a potential mechanism for differences in
theocean circulation between the present and LGM.
Observationalevidence, however, allows for an equatorward shift of
at mostabout 3◦ (18, 19), which in turn is here found to have
negligibleimpact on the solution (experiment “LGM windN” in Table
1).Proxy observations and climate models instead indicate a
slightpoleward shift and strengthening of the surface westerlies
overthe Southern Ocean (18, 19). A simulation incorporating a
3◦
southward shift and 20% strengthening of the Southern
Hemi-sphere westerlies shows a moderate increase in ice export
andassociated buoyancy loss around Antarctica (experiment
“LGMwindS” in Table 1). The increased buoyancy loss rate
amplifiesthe differences between the present and LGM simulations
dis-cussed above.
The loss of shallow shelf seas during the LGM has likely led
toincreased tidal energy dissipation in the deep ocean, which in
turnmay have caused enhanced vertical mixing (20, 21). On the
otherhand, the increased deep ocean stratification during the
LGMmay have suppressed vertical mixing, as more turbulent
kineticenergy dissipation would be required to mix the more
stratifiedwater column (22). In our simulations, which assumed
unchangedvertical diffusivities, the implied energy input to mixing
below theupper thermocline (300 m) almost doubles between the
presentand LGM simulations (Table 1, last column).
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Table 1. Summary of results from sensitivity experiments
Experiment∫
BdA N2deep ΨNADW ΨAABW zNADW zΨ=0 zAABWreturn ėmix
Present 0.4× 104 0.6× 10−4 17.5 5.2 1,450 2,050 2,370 0.53×
10−6
LGM 2.1× 104 2.3× 10−4 9.6 6.2 1,070 1,590 2,480 1.02× 10−6
LGM windS 3.4× 104 3.8× 10−4 9.5 7.2 1,000 1,500 2,530 1.42×
10−6
LGM windN 1.7× 104 2.0× 10−4 9.6 6.1 1,040 1,550 2,430 0.95×
10−6
LGM κ F02D 50% 2.3× 104 3.9× 10−4 6.4 4.8 810 1,250 2,490 0.73×
10−6
LGM κ + 50% 2.2× 104 1.8× 10−4 12.2 8.6 1,210 1,710 2,250 1.35×
10−6
LGM dTSH 1.6× 104 2.1× 10−4 10.9 6.2 1,120 1,660 2,520 0.98×
10−6
LGM dTconst 1.8× 104 2.2× 10−4 8.7 6.3 1,080 1,620 2,500 0.96×
10−6
Present seas 0.3× 104 0.4× 10−4 15.2 5.0 1,550 2,220 2,530 0.46×
10−6
LGM seas 1.6× 104 1.8× 10−4 9.9 6.1 1,190 1,750 2,410 0.85×
10−6
Warm 0 0.1× 10−4 19.9 — 2270 — — 0.35× 10−6
Each row indicates a different numerical simulation: Present
denotes the simulation with boundary conditions resembling
present-day conditions. LGMdenotes the simulation with reduced
atmospheric temperature, resembling LGM conditions. LGM windS
denotes a simulation with atmospheric tempera-tures as in LGM, but
also including a 3◦ southward shift and 20% strengthening of the
Southern Hemisphere (SH) westerlies. In LGM windN SH
westerliesinstead are shifted 3◦ northward (Fig. S3B). LGM κ-50%
and LGM κ + 50% denote simulations with boundary conditions
analogous to LGM but withdiapycnal diffusivities reduced or
enhanced by 50%, respectively (Fig. S5). LGM dTSH denotes a
simulation where atmospheric temperatures have beenreduced only in
the Southern Hemisphere, whereas LGM dTconst denotes a simulation
where temperatures have been reduced homogeneously over thewhole
domain by 5◦C relative to Present. Present seas and LGM seas denote
simulations analogous to Present and LGM, but with seasonally
varying airtemperature forcing (Fig. S1A). Warm denotes a global
warming simulation, with similar but opposite signed changes in the
atmospheric temperature as inthe LGM simulation (Fig. S3A). Columns
show various diagnostics:
∫BdA (in m4s−3) is the integrated buoyancy loss rate around
Antarctica (Materials and
Methods). N2deep is the mean stratification (referenced to 2 km
depth) averaged over the deep ocean basin below 1,500 m and north
of 40◦S (in s−2). ΨNADW
indicates the maximum AMOC overturning transport and ΨAABW is
the maximum overturning transport in the abyssal cell (both in Sv).
zNADW denotes themedian depth of NADW, computed as the depth (in
meters) at which the basin-averaged overturning streamfunction is
reduced to 50% of its maximumvalue. zΨ=0 is the depth at which the
basin-averaged overturning streamfunction changes sign; and
zAABWreturn is the depth where the streamfunctionreaches 50% of its
minimum value, thus denoting the median depth of the southward
return flow of AABW. ėmix is the globally averaged energy input
perunit area by vertical mixing below 300 m (in units m3·s−3).
To test the sensitivity of our results to the rate of
verticalmixing, we consider two additional LGM simulations in
whichthe vertical diffusivity is reduced or increased by 50% (“LGM
κ−50%” and “LGM κ + 50%”, respectively). Due to the
strongerstratification, the implied energy input to mixing below
300 mis still slightly larger than for present-day conditions in
LGMκ −50%, and the energy input is almost tripled in LGM κ +50%.
Reduced vertical mixing weakens and shoals the AMOCcell during the
LGM and increases the abyssal stratification—thus amplifying the
effects of atmospheric cooling. Enhancedvertical mixing instead
strengthens and deepens the AMOC celland reduces the abyssal
stratification—thus counteracting theeffects of atmospheric
cooling. However, even the simulationwith enhanced mixing maintains
a stronger stratification andweaker and shallower AMOC cell
compared with the simulationrepresenting present-day conditions,
indicating that the effect ofatmospheric cooling remains
dominant.
Significant uncertainty also exists in the spatial pattern
ofatmospheric temperature change between the present and LGM(14,
15). We consider two sensitivity experiments, which repre-sent
extreme cases: one where atmospheric cooling is restrictedto the
Southern Hemisphere (experiment “LGM dTSH” inTable 1) and one where
a globally constant cooling is applied(experiment “LGM dTconst”).
Both experiments show roughlysimilar results as the LGM reference
case with symmetric polaramplified cooling, as long as the
reduction in atmospheric tem-perature at high southern latitudes
remains about the same. Thisresult confirms our interpretation that
circulation and stratifica-tion changes are controlled primarily by
differences in the sur-face boundary conditions around
Antarctica.
The simulations here are highly idealized and, among
otherthings, do not include a seasonal cycle, which may affect
eventhe mean sea-ice growth and export rate around Antarctica.
Toanalyze the effect of seasonality, the present and LGM
simula-tions were repeated using seasonally varying air
temperatures,but leaving the annual mean temperatures unchanged
(experi-ments “Present seas” and “LGM seas” in Table 1 and Fig.
S1).Even though the idealized representations of surface
boundary
conditions, mixed layer dynamics, and sea-ice thermodynamicsmake
this model arguably less suited to represent the seasonalcycle, the
simulations do exhibit strong seasonality in sea-icecover around
Antarctica (Fig. S1B). Whereas the addition of aseasonal cycle
causes some minor changes in the deep oceancirculation and
stratification in both the present and LGM sim-ulations, the main
results regarding differences in the stratifi-cation and
circulation between the present and LGM remainunchanged by the
inclusion of a seasonal cycle (Fig. S1C).
To address the potential implications of our results for
long-term future climate change, we finally examine a “global
warm-ing” simulation (experiment “Warm” in Table 1), which
showsessentially reversed results from the cooling experiments:
Above-freezing temperatures around Antarctica lead to ice-free
condi-tions and net buoyancy gain. As a result AABW formation is
shutdown, leaving the entire deep ocean filled with nearly
unstrati-fied water of North Atlantic origin (Fig. S2). The effect
of thesepotential rearrangements on ocean carbon storage represents
animportant topic for future research.
Discussion and ConclusionsThe results of this study suggest that
atmospheric coolingalone—via a modification of the buoyancy loss
rate aroundAntarctica—leads to a strong increase in the deep ocean
strat-ification, a shoaling of NADW, and an increased
separationbetween NADW and the underlying abyssal overturning
cell.The simulated response of the deep ocean circulation and
strat-ification to atmospheric temperature change is consistent
withdifferences between the present and LGM inferred from
paleo-proxy observations (3, 6, 12, 13). A series of sensitivity
experi-ments suggests that the dominant control over circulation
andstratification changes is exerted by the atmospheric
temperaturearound Antarctica. Temperature changes in other regions,
aswell as differences in the atmospheric wind stress, instead
playonly a relatively minor role.
The results here are broadly consistent with some complexcoupled
climate model simulations (7, 8), as well as with globalocean-only
simulations under LGM boundary conditions (10).
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Coupled LGM climate simulations using the Community Cli-mate
System Model (CCSM)1.4 and CCSM3 show a stronglyincreased abyssal
stratification and shallower NADW (7, 23, 24).Consistent with the
results discussed here, these changes havebeen attributed to
enhanced sea-ice export around Antarctica(7) and ultimately reduced
CO2 concentrations (8). However,whereas Shin et al. (7) argue that
enhanced sea-ice export iscaused “ultimately by increased
westerlies,” (ref. 7, p. 1) we heresuggest that cooling alone is
sufficient and likely to be the domi-nant driver. Changes in
freshwater fluxes around Antarctica havealso been argued to explain
the high deep ocean stratification in adecoupled Community Earth
System Model (CESM)1.1.2 oceansimulation under LGM boundary
conditions (10). Many othercoupled climate models, however, show
different and widelydiverging changes in the deep ocean circulation
and stratifica-tion between preindustrial and LGM simulations (25,
26). Pos-sible reasons for this disagreement include differences
betweentransient and fully equilibrated solutions (27, 28),
insufficientincrease in Antarctic sea-ice cover and formation (29),
and/orcompensating effects due to other differences in the
boundaryconditions, such as changes in the ice sheets (26, 30). A
moredetailed analysis of comprehensive LGM climate simulations
isneeded to better understand differences between them, but
isbeyond the scope of this study.
The dominant role of atmospheric temperature change as thedriver
of differences in the ocean circulation and stratificationhas
important implications for our understanding of
glacial–interglacial climate swings. Although the exact mechanisms
arestill debated, it is likely that changes in the ocean
circulation andstratification have played a key role in modulating
ocean carbonstorage and thus atmospheric CO2 concentrations (31,
32). Ifocean circulation changes are themselves directly driven by
tem-perature swings, as argued here, they are likely to play a
cru-cial role in a positive feedback loop between global
temperature,ocean circulation, and atmospheric CO2. A better
comprehen-sion of this feedback loop will be central to our
understandingof past and future climatic changes.
Materials and MethodsNumerical Model Configuration. The
numerical simulations use the Mas-sachusetts Institute of
Technology (MIT) general circulation model (MIT-gcm) (33), in a
hydrostatic Boussinesq configuration. The idealized domainextends
from 70◦S to 65◦N, covers 72◦ in longitude, and is 4 km deep.
Thehorizontal resolution is 1◦×1◦ and the vertical resolution
ranges from 20 mnear the surface to 200 m in the deep ocean, with a
total of 29 levels. Theocean is bounded by a 1◦ strip of land on
all sides, which is interrupted onlybetween 69◦S and 48◦S, where,
above 3 km depth, zonally periodic bound-ary conditions give rise
to a reentrant channel, representing the SouthernOcean.
Atmospheric temperatures, net freshwater flux (i.e.,
precipitation–evaporation), and surface winds are prescribed in the
form of idealized ana-lytical functions shown in Fig. S3. Except in
the sensitivity simulations withseasonal cycle in air temperatures,
all atmospheric forcing fields are con-stant in time. Momentum and
sensible heat exchange between the atmo-sphere and the ocean are
described using standard bulk formulas (34, 35).In addition to the
sensible heat flux, an idealized radiative restoring is pre-scribed
as Frad = σ(T
4s − T
4a ), where Ts is the ocean/ice surface tempera-
ture, Ta is the prescribed atmospheric temperature, and σ = 5.67
× 10−8
W·m−2·K−4 is the Stefan–Boltzmann constant. In reality the ocean
expe-riences a net radiative heating, which is balanced primarily
by latent heatloss. Both are ignored here, which in effect
simplifies the thermal boundaryconditions to a restoring to the
prescribed atmospheric temperature—albeitwith a restoring rate that
is modified by wind speed and boundary layer sta-bility. This
idealization was chosen to avoid additional assumptions
aboutchanges in downward short- and long-wave radiation and
boundary layer-specific humidity. Moreover, use of a bulk formula
for moisture and latentheat transfer would require artificial flux
adjustments to close the globalsalt budget.
To test the sensitivity of the results to the details of the
thermal bound-ary conditions, additional simulations were performed
with a simple linearrestoring of the ice/ocean surface temperature
(36) (Fig. S4). The surface
heat flux is computed as F = 25 W/(m2K)(Ts − Ta). This amounts
to asomewhat faster effective restoring than what is on average
implied bythe original boundary conditions. To still obtain a
realistic present-day–likesimulation the meridional air temperature
gradient was slightly reduced,decreasing the air temperature at the
equator by 1◦C while increasing thetemperature at the highest
latitudes by 2.5 ◦C (which keeps the global meanair temperature
approximately unchanged). The air temperature differencebetween the
present and LGM simulations, however, is identical to that inthe
simulations discussed in this article. The results suggest that the
mainconclusions are not sensitive to the details of the thermal
boundary condi-tions (Fig. S4).
Sea-ice dynamics and thermodynamics are described using the
MITgcmsea-ice package, which is based on the viscous-plastic
rheology introducedby Hibler (37) and modified by Zhang and Hibler
(38) and Losch et al. (39).Sea-ice thermodynamics are based on
Zhang et al. (40) and use a zero-heat–capacity approximation, but
account for the different heat conduc-tivities of ice and snow
cover. Mesoscale eddy fluxes are parameterizedusing the Gent and
McWilliams (GM) (41) and Redi (42) parameterizations,with a
variable eddy diffusivity formulated following Visbeck et al.
(43),with α= 0.01 and mixing length l = 160 km. The eddy
diffusivity is cappedbetween Kmin = 200 m
2·s−1 and Kmax = 2,000 m2·s−1, and the GM param-eterization is
tapered in the presence of steep isopycnal slopes, followingGerdes
et al. (44). Diapycnal mixing is represented by a vertical
diffusiv-ity, which is strongly enhanced in the abyss, but reduces
to a backgroundvalue of 2×10−5 m2·s−1 in the thermocline (45, 46).
The diffusivity profileis shown in Fig. S5. Convection is
parameterized using a diffusive adjust-ment with a convective
diffusivity κconv = 10 m2·s−1 whenever the stratifi-cation is
statically unstable. Dissipation of momentum in the bottom
bound-ary layer is represented by a linear bottom drag, with a
piston velocity of1 mm·s−1. No-slip horizontal boundary conditions
are applied at the walls,and grid-scale noise is suppressed using
Laplacian and biharmonic viscosi-ties, with viscosity coefficients
ν2 = 2×104 m2·s−1 and ν4 = 2×1013 m4·s−1,respectively.
All simulations are integrated to equilibrium for at least 4,000
y, and aver-ages are taken over the last 500 y of each simulation.
Whereas the simula-tion with present-day forcing reaches a steady
equilibrium solution, the coldLGM simulation exhibits some decadal
to centennial variability in the AMOC.The exact nature of this
variability, which appears to be associated withsea ice in the
North Atlantic, is beyond the scope of this study, but may
beaddressed in follow-up work. The magnitude of the variability is
small com-pared with the differences obtained between the present
and LGM simula-tions and is averaged out in Figs. 1–3.
Nevertheless, the lack of a steady-statesolution puts into question
the use of an accelerated tracer time stepping(47), which has been
used to speed up the equilibration. To test the impactof the
accelerated tracer time step, the LGM simulation was initialized
fromthe statistical equilibrium solution obtained with tracer
acceleration andintegrated for another 1,000 y without tracer
acceleration. Whereas prop-erties of the internal variability
appear to be affected by the tracer accel-eration, the mean state
and circulation discussed in this paper are virtuallyunaffected.
The sensitivity to tracer acceleration was also tested explicitly
inthe present seas simulation, which includes a seasonal cycle in
the thermalforcing. Again, no significant effect on the deep ocean
circulation and strat-ification (or on the seasonality of sea ice)
was found. Due to the negligibleeffect of tracer acceleration on
the mean state and circulation, all sensitiv-ity experiments
discussed in this study use tracer acceleration for the
entireintegration.
Computation of Buoyancy Loss Rates. Buoyancy loss from the ocean
is com-puted based on the net heat and freshwater fluxes as
B = gαQρ−10 C−1p + gβFSρ
−10 , [1]
whereQ is the net heat flux and F the net freshwater flux out of
the ocean(which include the effects of sea-ice formation and melt),
α is the thermalexpansion coefficient, β is the haline contraction
coefficient, g is the grav-itational acceleration, ρ0 = 1,035
kg·m−3 is a reference density, S is thesalinity, and Cp is the heat
capacity of seawater. Because we are interestedin the effect of
surface fluxes on the density of a parcel at depth, the
thermalexpansion and haline contraction coefficients are computed
for an ambientpressure of 2,000 dbar.B is generally positive
(denoting ocean buoyancy loss) within a strip
around Antarctica, but negative farther northward in the
circumpolar chan-nel. The “total buoyancy loss rate around
Antarctica” is computed byintegrating B over the entire region of
buoyancy loss around Antarctica,defined to include every gridpoint
south of 55◦S where B> 0 (because the
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areas of buoyancy loss and gain are well separated, the results
are not sen-sitive to the exact choice of this latitude).
ACKNOWLEDGMENTS. I thank Alice Marzocchi, K. Thomas, and two
anony-mous reviewers for their very valuable comments. The MITgcm
config-
uration files and model output data are available from the
authorupon request. Funding for this work was provided by the
National Sci-ence Foundation under Award 1536454, and computational
resourceswere provided by the Research Computing Center at the
University ofChicago.
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